{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.empty((100, 2))\n",
    "X[:, 0] = np.random.uniform(0, 100, size = 100)\n",
    "X[:, 1] = 0.75 * X[:, 0] + 3. + np.random.normal(0., 4, size = 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a18f5a710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, iterated_power='auto', n_components=1, random_state=None,\n",
       "  svd_solver='auto', tol=0.0, whiten=False)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(n_components=1)\n",
    "pca.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_reduction = pca.transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.79988513, -0.60015313]])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.components_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 1)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_reduction.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_restore = pca.inverse_transform(X_reduction)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a18f62940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_restore[:, 0], X_restore[:, 1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 手写识别练习"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "digits = datasets.load_digits()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = digits.data\n",
    "y = digits.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "noisy_digits = X + np.random.normal(0., 4, size = X.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "noisy_digits.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797,)"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "example_digits = noisy_digits[y == 0, :][:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 64)"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "example_digits.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 64)"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for num in range(1, 10):\n",
    "    x_num = noisy_digits[y == num, :][:10]\n",
    "    example_digits = np.vstack([example_digits, x_num])\n",
    "example_digits.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a19083128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_digits(data):\n",
    "    fig, axes = plt.subplots(10, 10, figsize = (10, 10),\n",
    "                            subplot_kw={'xticks':[], 'yticks':[]},\n",
    "                            gridspec_kw=dict(hspace=0.1, wspace=0.1))\n",
    "    for i, ax in enumerate(axes.flat):\n",
    "        ax.imshow(data[i].reshape(8, 8),\n",
    "                 cmap='binary', interpolation='nearest',\n",
    "                 clim=(0, 16))\n",
    "    plt.show()\n",
    "    \n",
    "plot_digits(example_digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, iterated_power='auto', n_components=0.6, random_state=None,\n",
       "  svd_solver='auto', tol=0.0, whiten=False)"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(0.6)\n",
    "pca.fit(example_digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "components = pca.transform(example_digits)\n",
    "filtered_digits = pca.inverse_transform(components)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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f6/qqXbt2wZy1oKhRowbMmzRpQueIj4+Hue/+FRYWwnFc+8faquTk5NDnIC1btqSPpaSksDng/pn9to8+x0QoFKr0thVyc3NhXq1aNZg3bdqUjsU+w9zcXLiPqamp4QYNGkRsz9qtoFYOFWrXrg3z5cuXe21fr149OkdRURHMly5dSo9R1C6grKwMjoNaHVRgnwdrhcKOhdatW9M5fL+DZmbp6enhxo0bR+SsXYerzU7NmjVhvmTJEpiz1+vaR2TdunWWn58P3zB2nmH74WoVxD5ftn9M586dvbY3q7rfCZedO3fC3Pd3wtUihfm982hV7SNrF8JabLCWIK7fCvQc1zEa8fzKbFQhOzvbFixY4PMUauzYsTC/9NJLYT5w4ECYjxkzxnvuUCgEr4b33T/2AZuZTZ48GebnnHMOzFkPF9b/yMysfv36MHft3/fffx+Rsx9210KIvV7fhYXr8zvhhBPYHLSaISsry7755puInPWiiaYPT0JCAszbtWsH8/fee4+OVbduXZgnJyfDfWzQoIGNGzcuImcL0x9++IHOffbZZ8P8pJNOgvmAAQNgftttt9E52D9smjdvDvcvMzMT9uPbu3cvHIf1WDMz69ChA8zZwo0tEqZOnUrnOOKII2DuOkYbN25s06ZNi8hXrFgBt2f7bmZ2yimnwLxRo0YwZ693/vz5dA6kS5cu9DF2HmX/4GILVjOzLVu2wJyd+5hofrd8fyeiWehNmjQJ5meddRbM2Xl3+vTpdA7GdYxW5W896t9pxvuT1amDC71mzJhB50D98FzH6MH0X2MiIiISWFoIiYiISGBpISQiIiKB5X+BBMAukGXXUpi5/98U2bZtm9f2fwXX/rH/i2fXpPz4448wZ9d+mLmvHWDQ++7zf6kVvv32W+/nIKWlpVUyToVQKGSJiYlVMtbChQthPmjQIJg3a9YM5q7rkJYuXer1mpKSkuBFg2yf2WsyMxs1ahTM2cXE7BoP1zVCeXl59DEkJiYGXiSfnJwMt3ddK/LVV1/BfOvWrTBnF7W7zlWs6MOlvLwcXl94zDHHwO1dxw+7/mzDhg0wZ9d/uRQUFERk0XxvN27cCPPmzZt7P4c59thjvbavSqzIID09nT7HdSE8wr4H/z9j5zhWCMQKo3bv3k3nQO/9vn37KvHqfqO/CImIiEhgaSEkIiIigaWFkIiIiASWFkIiIiISWFoIiYiISGBVSdUYu43+jTfeSJ+D7nBsxquk2O39XViVy1/hmmuugTm78zK7i/OaNWvoHK6KIB/sNu+sTYiZ2emnnw7zL7/8EuasuoXdzTda+/fvh7ffZy0E2B3Azfhdr1krBFYh5arUcd1VFykrK4PVEKxqzNXy5M4774T5sGHDYP7RRx/B/IsvvqBztG/fnj7mg7VUcFXd3XHHHTBnd11m7Uj27NlD53BVPDEJCQnwNbAKokWLFtGx2HmGVaCxu7Wzc7gZrnqK5o7sc+fOhfnzzz9Pn/Ppp596zeH6rP5s7Lhi1YtmZkOGDPGao2HDhl7bm1Xt7yC707frfb/nnntg7tsmxdUuCJ1HfSrT9RchERERCSwthERERCSwtBASERGRwNJCSERERAJLCyEREREJLC2EREREJLCqpHy+c+fOMP/hhx+8x2JN5R555BHvsXxLk33NmTOHPhYbGwvz7OxsmP/73/+G+dFHH+39uph9+/bBZqmbNm2C259zzjl0rDZt2sC8b9++Xq+JlaibmS1YsMBrLLPfjh9Usv3GG2/A7VmpuBlv4MjKnAcMGADzXr160Tl8G+eGw2ErKSmJyD/44AO4/YMPPkjHevTRR2F+9913w7x///5euRlu2BkN1kDxsssuo8+58MILYT5u3DiYs1tbZGVl0TlYc1OXcDgMb8EwZcoUuP3tt99Ox+rZsyfMp06dCvOaNWvC/Nprr6VzVJWuXbvC/IorrqDP6dixo9cc7PYr7PYkZvxz91WjRg2Yu44RNnfv3r1h7mpwzPzZv4Nm/Dtlxn8LGVZuzxqZm+Hb6/g0qNVfhERERCSwtBASERGRwNJCSERERAJLCyEREREJLC2EREREJLC8qsbC4bAVFxdH5Kzx4bJly+hYrCkgu8L8zTffhLmr6sdXeXk5bB63evVquD1rdGlmVq9ePZhv3rwZ5r/88kslXuEfk5ycbO3atYvIu3XrBrd/55136FisIvDHH3+E+SmnnFKJV/jfMjIyvJ/DoMaRZmZdunShz2GvmR2L0TSQ9X1OfHy81alTJyI/77zz4PZpaWl0rBkzZnjNfcMNN3htb2a2e/dur+3D4bCVlpZG5HXr1oXbf/zxx3Qstu+s+SerSmEVa2bRNcEMhUKWlJQUkQ8cOBBun5qaSsdav349zFnVGDp//x60/6xy0uXnn3+G+fLly+lzJkyYAPOFCxfCnDUF3bFjB53D9R1B2O8gO/d16tSJjsWOn40bN8L8hRdegPmoUaPoHFVp/PjxMHdV3rHz+MknnwxzVino00TVl/4iJCIiIoGlhZCIiIgElhZCIiIiElhaCImIiEhgaSEkIiIigeVdNYb6HLGr7r/++ms6Fqueqko5OTle28fExMB+MR06dIDbT58+nY41ePBgmI8ePdorv/nmm+kcvmJiYmAvHlaxxvbbzOzzzz/3mnvFihVe25v5f34VUEUL6wPGcpfrr78e5qy6h21v5q48ZFD1BKu8adGiBR2H9TNiff22bdtWiVf333wrckKhENw/1jfozDPPpGMtWbIE5gkJCTA/++yzYY76GFWI5rhm8vPzYe7qVedb+ffSSy/B3FW1iiqCUGXf/35s+/btEXnTpk3h9kceeSQdi1VoMuz9cB2H8+fP95rDDPcua968Odx23rx5dBx2XLP+ZKyykB07Zv7fQZczzjgD5qyq08yse/fuML/yyith3rhxY5izPnlVQX8REhERkcDSQkhEREQCSwshERERCSwthERERCSwtBASERGRwPKqGjtw4ACsTsnOzobbs/5OruesW7fOK3fp3Lmz1/alpaVWUFAQkaNKMjP3/qWkpMCcVWewKgHWO8eM9zPzlZWV5T03qwBh8vLyYD5r1iz6nFNPPdVrjgqo6mjTpk1wW9ZfKhqokuT3RFOJhbRs2RLmc+bMoc9h1RnMG2+8AfPTTjuNPod9d1zQ51etWjXvcVi1FzsWWRXobbfdRueIptcYE01VTP369b22f/fdd2Huql4cMmRIRBYXx3864uLiYKUS65/l0qhRI5izPpZfffUVzJs0aULnaN++vddrKi8vt6Kiooic9TPr2rUrHYvtH6t+Y/3aGjRoQOeoyp6N7Lvj6j3H9p99P2fPng3zHj160DlQFaPP+Vh/ERIREZHA0kJIREREAksLIREREQksLYREREQksLQQEhERkcDSQkhEREQCy6t8vlq1atapU6eInJUNuspz586dC/OHH34Y5q5SdQaVwrvExcV5zeMqd2VNSfft2wfzoUOHwtxVIl9cXOx4dX+ca/wHHngA5qyB4e7du2HOGvKZ8RLZaLAyeVfz34ULF3rNwcrLXVy3KPBRWFgIc9fx88MPP3jNccwxx8A8NjaWPiea214gqFmwmfv2AD179oQ5a0R7/vnnw9xVWv7TTz/Rx3yxZrCuBsf9+/eHOftesXN1x44d6RzfffddRMbOYy7sVgpr1qyhz5k2bRrMH3roIZivXr0a5q7bVPg2AI+NjYXnfvZ74DpGWVNtdnuC+Ph4mLtu44Aa4EaLnUddtydgpfWoma8ZP8+4oGMI3eKA0V+EREREJLC0EBIREZHA0kJIREREAksLIREREQksLYREREQksEI+jclCodA2M8NdQw8tWeFwuM7BofbvkAH3z+zw30ft3yHjcD9GD/f9M9MxeqjvI92/g3kthEREREQOJ/qvMREREQksLYREREQksLQQEhERkcDyarGRkZERzszMjMhLSkrg9q5b7+/duxfm7HbnbCx2u3wzM3b9U25ubj66iCo9PR3uHxuH3TrczGzlypUwb9q0KcyTk5PpWAx7D5cvXw73LyMjI5ydnV3p8V230f/5559hfuSRR8Kc3V7fpaysDOaLFi2C+2fmv4+uz3Djxo0w37VrF8zZLfbZbenN+LG1ZMkSuI+pqanhBg0aRGzP9qO0tJTOzW7jn5eXB/O6devCPC0tjc7B5l+8eDHcv7S0tHCjRo0itmftJ1xYawF2jmGfX0ZGBp2Dtd9g55j/GQ8eowcOHIBjuc6j7NzL2tPUrl0b5s2aNaNzoM8wLy/PCgoKYI8Etn+svYfr3MdaSixatIg+B+ncubPX9mZmOTk59DyalZUVsT1r6eA6dtnnt3TpUpiz98r1O8jeQ7Z/Zvy3kB2L7LfIjP8WHn300TCPifH/+8z+/fsjso0bN9qOHTtwH4+DeC2EMjMzYd+UDRs2wO1TU1PpWKzX2IgRI2DOfkhdfXjYiSU5ORleDZ+ZmWkzZ86MyNmPjGuh0K9fP5iPGzcO5u3bt6djMayHzfHHHw/3Lzs72xYsWFDp8VnfMDOzbt26wfyFF16Aee/evSs9b4WdO3fCPDU1lVYz+O4j+gJVePDBB2E+adIkmJ966qkwv+++++gcbLFXv359uI8NGjSw9957LyLfs2cPHMfVb69OHVxQceutt8J8yJAhML/wwgvpHGz+jIwMuH+NGjWC7y86KZu5T5pjx46F+RNPPAFz9vldfvnldA7HP2y8j1H2jwvXPyLYoq5Lly4wP+mkk2A+YcIEOgdaULq+z9nZ2bA/GZuD/SCa8WPUtfhGXOcEdn6PjY2Fn2FWVpZ9++23ETnrmebqucl6DbLjii14pk6dSudg/xALhUL0GM3MzLQZM2ZE5Ow3ffbs2XT+M844A+ZsDRDNHwUWL14ckV100UWVfr7+a0xEREQCSwshERERCSwthERERCSwtBASERGRwPK6WLqsrAxe+c+qT3766Sc61kcffQTzJUuWwJxdmMyqI8zMiouL6WNIOByGF86xC/NOPPFEOlYohC9WZ1Ub0ahevbr3c1CV0tatW+G2119/vff433//PczZBZ9du3alYyUlJXnPX15eDi+AZhfgffPNN3SsH3/8EeZNmjSB+ciRI2Hu2kffaqhQKAQvEG7bti3c3nWhLasC27ZtG8zRBaJm7otB2QXvTFxcHHxd0VSSjBkzBubNmzeHObuYl21vhi/S/D3hcBgWcrALwqtVq0bHevvtt73mnjhxIsxXrVpFn/PLL5HX1LqKDEpKSuBF3G3atIHbs0pTM7NXXnmFPuZj1qxZ9LH09HTv8dD5nVXesd9HM7PXXnvNa172+8gKZ8yi27/S0lJ4kTw7Fl2/Fbt374b5m2++CfPu3bvDvEOHDnQOVCzCClEQ/UVIREREAksLIREREQksLYREREQksLQQEhERkcDSQkhEREQCy6tqLD4+3ho2bBiR5+bmwu1dfY5YNQnr68PGat26NZ3DV3Fxsa1fvz4iZ5UZ7Pb2ZrzyhlWaPf/88zBn1UBmZvXq1aOPMajagVUcsNvbm/Gqv48//hjmrPKuqqvGYmJivG7R3qdPH/rYu+++C/P69evDfMqUKTBHvcEqdOrUyfHqIiUlJdlRRx1V6e1Z/yMzs5YtW8KcVUKddtppMHf1axswYIDj1UWKiYmBlSmsXY7rGOnVqxfMBw4cCHP2WbiOJ9ZexHV7/1AoFNWxjbCeVKxakLViYVWuZvg74qpGZL8TmzZtos9hfCp/zHiFFjsWohEKheA8hYWFXq/JDFfkmZkNGzYM5o8//jjMXS1HomlvlJiYCKvg2LmhVatWdCz23q9YsQLmrFWJq2rsj/Yn1F+EREREJLC0EBIREZHA0kJIREREAksLIREREQksLYREREQksLQQEhERkcDyKp9nWNnpl19+SZ9z7LHHwpyVZd9yyy0w/+GHH+gc7dq1o48h1apVgyV6n332GdzeVSLLsIadKSkp3mO5yrJ9sBJ2V7NHdjsD1kTQt4w6WqyhZTTlyuw57BYBrHze9dmiJrgue/fuhbc7YA1Uc3Jy6Fjsu/bII4/AfNGiRTBHpdIV8vPz6WNIaWkpvPUEavZsxkttzcxOOOEEmF922WVer8lVtrt8+XKvscx+u01HXl49CGN1AAAgAElEQVReRO5qXsu8+uqrMGeNNtetWwdzdl6KRmlpKfzc2a1RWCNYM7PrrrsO5lOnTvUay9VU1tVUFzlw4AAs/Y6NjYXbs++ZmdnDDz8M8xdffNHrNblupYKOtWgdffTRMGe3GjEzGzduHMyvvfZamJeUlHi/ruzs7IhM5fMiIiIilaCFkIiIiASWFkIiIiISWFoIiYiISGBpISQiIiKBVSVVY6xxnAurKOvYsSPMWaVHNNVWvm644QaYu5quLlu2DOY//fSTV+6qDFu9ejV9zAerDjv11FPpc1gDTlZhw6o2qrKaw4w3tGSNgVlFoJnZ6NGjYX766afD/JRTToH51q1b6Rw1a9akjyGs6Spruvj111/TsXr27Anzn3/+GeasWm737t10ju3bt9PHkLi4ONjsd+3atXD7uXPn0rFYI2NWgfbKK6/AfMuWLXQOVK3ye8rLy23v3r1e2zPHH388zL/99luYz5w5E+au6r7atWtHZK5qx7KyMtu1a1dE3rRpU7i9qzEwq0Jl1WGsCS5r2mtmVlBQQB9DYmJi4DnG1biWYcfoE088AfObbroJ5q7v2V/xG+n6LXrmmWdgzqpTGVf1WzQVl/+b/iIkIiIigaWFkIiIiASWFkIiIiISWFoIiYiISGBpISQiIiKBVSVVY2+88QbMWeWCmdkXX3wB87///e8w79Kli/frYn11mOLiYvicjRs3wu2Tk5PpWIsXL4b5/PnzYc6qsFwVI61bt6aPIWVlZbZz586InH1OrmoZVn3CegOdf/75MP+jV/tX1oIFC2D++OOP0+ccc8wxMGefFatGYn3AohEXFwcrxO655x64Pas+cbnyyithfuaZZ8J8/fr1dCxXZaUPVvU3e/Zs+hz2ebC+d6wXVp8+fegc+/fvp48xSUlJ8Lv75JNPwu3vvvtuOhY7B1166aUw79WrF8xdnxOqcCsrK6PbJyYmWrNmzSLy++67D27vqvxjny/7DN955x2Yu/pXzZgxgz6GJCQkWGZmZkTO+r6xyjczfvxcfPHFMGfHYufOnekc0VR1m+HfHlZJ+/bbb9NxUlNTYc56XDKoErGCqsZEREREoqSFkIiIiASWFkIiIiISWFoIiYiISGBpISQiIiKBVSVVY3/7299gPnnyZPocdNW9mdn48eNhzipW4uL4LnTq1Ik+hiQkJMDeQawv0NVXX03HclXSIKz32kcffUSfw953pqSkBFaHoAoPM7NRo0bRsVjvnhUrVsD8+++/h/knn3xC5zj33HPpY0x5eTmsxGDHz/XXX0/HateuHcx9+zWxahkz9/HrY8SIETB///336XMSEhJgzqpcWrZsCXPXPtxxxx30MR/sc/rqq6/oc4499liYo8pJM96XDfXaquCq1vF11113wXzChAn0OayP1FtvvQXz6tWrw7xNmzZ0jptvvjkii+a4ffTRR2F+++230+ewqrFPP/0U5qw6lFUdmvFKV19XXXUVzFnvPjPek5J9b1lfNldV3KBBg+hjTElJCawaZpVeQ4cOpWO1atUK5qzKjvUVdPXDQ33sXBXXB9NfhERERCSwtBASERGRwNJCSERERAJLCyEREREJLC2EREREJLC0EBIREZHAqpLaXdZU8sUXX6TPqVGjBszffPNNmP/73/+GOStZNONl775YY7zhw4fT55xzzjkwZyXIrIkgK5c04w3wmKSkJFjKyMrBXSWR27Ztgzm6/YAZL/U/44wz6BxDhgyhjzExMTGwEeXu3bvh9qwxpxn/fFkTXvaeVFWJfDRWrVpFH5s2bRrMn3vuOZg/88wzMH/ooYf8X5gnVoI8btw4+hxWDs9uNTB27FiYH3fccXSOpKQk+hgTDofh7SfYWN988w0da+LEiTBn5z62j++99x6dw1dxcTG8fQi7ZcrgwYPpWKxp8LPPPgvzO++8E+Znn302ncMXu0UHa4DranzMGqKyprm//vorzLOysugc0YiPj7cjjjgiIme3hWHHoRk/j7PG5KyBq+t2MdWqVYvIYmIq/3ce/UVIREREAksLIREREQksLYREREQksLQQEhERkcDSQkhEREQCKxQOhyu/cSi0zczwZe6HlqxwOFzn4FD7d8iA+2d2+O+j9u+Qcbgfo4f7/pnpGD3U95Hu38G8FkIiIiIihxP915iIiIgElhZCIiIiElhaCImIiEhged37PyMjI4xaKLDrjDZt2kTH2rdvH8xjY2NhXr16dZjXq1ePzsHk5OTko4uo2P6Vl5fDcVirBTOzsrIymG/fvh3mrOVI48aN6RyJiYkw990/Zt26dfSxwsJCmLN2JBkZGTBn+21mlpaWBnO2f/8zD9xH9rpcLShSU1NhzsZi++I6RkOhEMyr6jPMy8ujj7GWIPXr14c5a6XDjnUzfm748ccfvfavpKQEjuPaP3aLffZ6U1JSYO76/EpLS2G+ePFi72OUvS7WXsSFtetgnyE7v5oZbAeyceNG27lzJzx4fffPdR5Fc5vx7yBqtWDGW/+Y8d+c3NzcP/08ylqhsO8Na1PC2nuY/dYuA2H7Z+b/W79lyxY6/549e2DO2h6lp6fDHLX8qIA+w7y8PCsoKMAn2IN4LYSys7NtwYIFETk7ST388MN0LDSOGf8x6datG8zvuOMOOgcTCoXg1fBs/9gH6do/9iGzXj8nnngizEeOHEnnaNq0Kcx994+54oor6GOsT8ySJUtgPnDgQJifcMIJdI4LL7wQ5nFxcbSage0je11nnXUWnZ/1i1u2bBnM2Wd4++230znYSaqqPsPbbruNPvbCCy/A/Nprr4X5TTfdBHN2rJvxH79WrVp57R/7sXTtH/tx37VrF8x79OgBc9c5hv3DJj093fsYZa+rZ8+edH7H+wtz1vepS5cudI6VK1dGZBdffDHdnu0fO07uv/9+r7nNzJYuXQrzDh06wPw///kPnaNmzZowT05OrpLvoKsfJuuHV1xcDHPWY61t27Z0DvYPm4SEBO9jlPW+ZK/LzGzGjBkwnzp1KszPPPNMmP/jH/+gc6DPsG/fvnT7g+m/xkRERCSwtBASERGRwNJCSERERAJLCyEREREJLK+Lpc3wxXnsgrbNmzfTcTp37gzzN954A+YtW7asxKv7c8TF4bfpmGOOoc9hF8G++eabMJ80aRLMR4wY8Tuv7o9jF7uziiYzs06dOsG8Y8eOMH/55Zdh3r17dzrHjh076GNMcXGx/frrrxE52xd2QbaZWUFBAcxnzpwJc3ZRveuC3j8bu7DbjF/Azo53dhH1W2+9RedgF1cy4XAYVmIlJCTA7Y888kg6FqsCe/DBB2E+YcIEmF9//fV0Dle1lS92jHbt2pU+h70vr776KswnTpwI87Vr19I5atWqFZGxSisXVtHFLlY248Uip556Ksw/+eQTmLPKXzNeYedr9erVMG/QoAF9ztChQ2F+yy23wPy0006D+V/VIYJVKru+h7169YL5d999B/PXXnsN5q6L6lGFMTuPIfqLkIiIiASWFkIiIiISWFoIiYiISGBpISQiIiKBpYWQiIiIBJZ31RiqFqhTB7Yrcd4aftasWTBnvYP69Onz+y/uDwqHw/DW5qyPC2vBYMZvOc7GuvTSS2HOqs+iUVRUBCv8WrRoAbcfM2YMHYtVYbDbqa9ZswbmrooR1p/s96DKxnbt2sFtGzVqRMdhFVfsfWHVSKyyJxqlpaWwmo1VuN199910rN69e8OcfW/ZHOyzNePnBiYUCsFqD9ZKwtW+ICcnB+asf9WgQYNg7voOsioal5KSElhRy6rGWAWYy0svveS1Pet5ZYbbN7j2u7S0FPaxY1U8rmP0l19wFwhW5XbrrbfCvCqr+xjWW9NVXVxVr8vVM7F58+be4xUVFcH3mJ33Xa2KGFYV3KZNG5i7jlHWV7Cy9BchERERCSwthERERCSwtBASERGRwNJCSERERAJLCyEREREJLC2EREREJLC8y+cRViKbmZlJn8PK5xs3bgxz1nTV1SywSZMm9DGkpKTENm7cGJFnZ2fD7fPz8+lYCxcuhDkrFz/vvPNg3qxZMzrHrl276GNIQkICfH/Ze5iamkrHeuCBB2C+YsUKmLP9aNWqFZ0jmqar8fHxsMnh1q1b4fZ169alY23ZsgXmJ554IsxHjx4Nc1fTxdatW9PHkLi4OEtPT4/ICwsL4fasRN6MNxmdO3cuzFkDzA4dOtA5fJWXl8PmtfXq1YPb79+/n47Fmnwyffv2hXk0JfIusbGxVqNGjYi8Kku82TmLNRhFJfJ/BCpnZueTDRs20HGmTZsGc/bbMnz4cJij97uCqyzbB7vtxNdff02fc/zxx8OcHQv79u2DeTQl8i7x8fHwd53dIgA1uq7AblFyySWXwPzHH3+EObsFihm/vUZl6S9CIiIiElhaCImIiEhgaSEkIiIigaWFkIiIiASWFkIiIiISWFVSNVZaWgrzpk2b0uew5pwLFiyA+Y033ghz1tw0GqziiHE1Bb3gggtgzq66nzdvHsxPPvlkOketWrUcrw5DTXNZVczTTz9Nx2FN/lAzSTOzjh07wpw12DPjDf6iwarDtm/fTp8zcOBAmLNqq7Fjx8Lc9T5Wldq1a3s/h1WzsCowVplWlWJiYpwVPgdjTYzNeCUUa9S6fv36Ss/7R7Cmq64KUWbx4sUwZ1VVWVlZMHdV3aDzezgcptvHxcU5K04P1rBhQ/rY7bffDnN2/mENkV2NXVNSUhyvLtLevXttzpw5EXmPHj3g9qwyzIxXT59++ukwf//992FeVFRE54im6pE1XXVVbjGsspOdL1nFowuqpvOpJNNfhERERCSwtBASERGRwNJCSERERAJLCyEREREJLC2EREREJLC8qsZKS0thlU1aWhrcPhQK0bFQ9ZIZ77nFqsxGjRpF53jyySfpY0goFLKEhIRKb//dd9/Rx4455hiY33XXXTBnFUqsr9XvPYaEQiGLj4+PyFml3NChQ+lYqN+Vmdlzzz0H8yFDhsD8/vvvp3P49oqq4FNtxo5dl7feegvm5557LszvvPNOOtaHH37oNXc4HIZVPD6VVhVY77DrrrsO5lOnToX5fffd5z03Ew6Hrbi4OCJnveJ27txJx2L9CdmxOHPmTJh/+eWXdA7Wn8wlMTERVtT+8MMPcHtXT8Hu3bvD/JFHHoH5F198AfO8vDw6B6ricZ3by8rKYL+4aKpcmT59+sCc/X6w7c3MOnfu7DV3cnJyVNVTCKuuc/VgRKq6H15CQoKzV+jB0OddgfVH69WrF8xZJZ0L6uHJ1hiI/iIkIiIigaWFkIiIiASWFkIiIiISWFoIiYiISGBpISQiIiKB5VU1xio61q1bB7dfs2YNHeurr76CeZMmTWA+ZcoUmLuu3nf1w0FKS0utoKAgImcVUkuWLKFjsQqQ6dOnw5xddc+2N3P3sEHC4TDsScMqDlhfNDN+Zf+WLVtgPnjwYJi7KsNKSkroY0woFIL7s2PHDri9qyfSuHHjYP7tt9/CnPVM2rBhA52D9eljSkpK4OcSE4P/TbNw4UI6FnsOq9Bi300X1K/IhVVusu/ga6+9Rsdiz2H9mth+n3/++XQO38rNCqjqip3LXH2yZs+eDXNWMcvOGV26dKFzoD59rsrM8vJy27t3b0TOqsZcvfjq168P81deeYU+B5k4cSJ9zLfHW1lZme3evTsiZ/vH+i+amX3yyScwf+ihh2AeTeWdqw8ZExsb69WD7ZtvvqGPsffetzqMnY/NcJ83tFZh9BchERERCSwthERERCSwtBASERGRwNJCSERERAJLCyEREREJLC2EREREJLC8yufj4+NpOSNy0UUX0cfKyspgnpSUBPPevXvDfNCgQXQO37LBuLg4q127dqW3nzt3Ln1s8uTJMM/IyIB5v379YO5qfMrKnxlWWs48//zz9LEXX3wR5qxM/qmnnqr0vBVQg9jfw0p3WZm863hOTk6GOWuo27FjR5i7jlHfWwQkJCRY48aNI/I5c+bA7T///HM61ujRo2Hes2dPmLPmlK7bA0RTco+wz8JVgstub9GoUSOYt2jRAubs/TCL7hgtLS21/Pz8iJyV+y9btoyO9emnn8KcHaOsJJrNbYZvceE698TExFj16tXp4wcbP348fYzdqqJevXowZ78Tl1xyCZ3D55zv8uuvv8L80Ucfpc95+eWXYX7cccfB/IILLvB+XdE0ZD1w4ICtWLEiIm/dujXc/qeffqJjvfTSSzBv3rw5zOPi8LKE3Z7EzCwrKysi82mgrr8IiYiISGBpISQiIiKBpYWQiIiIBJYWQiIiIhJYWgiJiIhIYIV8GpOGQqFtZvbLn/dy/jJZ4XC4zsGh9u+QAffP7PDfR+3fIeNwP0YP9/0z0zF6qO8j3b+DeS2ERERERA4n+q8xERERCSwthERERCSwtBASERGRwPJqsZGRkRHOzs6ukonXr18P8+3bt8O8ffv23nOw28Dn5OTko4uoUlNTw+g23qzth0tBQQHMt27dCvMjjzwS5gcOHKBzsNvYs/3LyMgIo1uRh0IhOgezY8cOmLN2C6ytAWudYMZvDc/2z8wsLS0tjObyud16BXaMss+Etetwvb81atSAueszrKrv4J49e2CObq1vZtayZUuYs7YNLmz/ateuHUbvI5sDtVOpwL6D5eXlMGftQFxtUFg7gNzcXHqMpqenh1GbFDZWaWkpnX/btm0w37dvH8zZ99D3HLdu3TrLz8+HB3ZGRkY4MzMzIvdtCWRmtnv3bpivWrUK5m3atIE5e2/NzGJjY2H+f/kd3LhxI8ybNWsGc9f+Ma7zqO8xumvXLjoPaz3CvodNmzaFuev4Qb8jrmP0YF7vXnZ2ti1YsMDnKdTNN98M87fffhvmrK+X62Jv1CPHzCwUCsGr4Rs2bGjvv/9+RH7UUUfBcdgHaWY2duxYmLP+XVOnToU5+8KbmXXt2hXmbP+ysrJs3rx5EXk0iwT0PpmZ/f3vf4f5E088AfO2bdvSOVjvJ7Z/Zr+d6D/55JOIHC0Af8+NN94I859//hnm9957L8xd/ah69eoFc7aP7DvIevexk7yZ2cyZM2HO+jWxvkjHH388nYNh+1e/fn37z3/+E5Gzfl+sx5qZ2RtvvAFz1oPwzTffhDn7UTLjvQMTExPpMdq4cWObNm1aRF63bl24PfvHoRnv+ffNN9/A/Mknn4Q56yHFdOnShT6WmZkJPxd2PnZh58WBAwfCfNKkSTBPS0ujc9SqVQvmvt/BaLDv4AMPPADzCRMmwLxOnUoVR/0X13m0cePGNmPGjIicvY+s552Z2d133w3z/fv3w5x9D12/U0cffXRE5jpGD6b/GhMREZHA0kJIREREAksLIREREQksLYREREQksPwvNQdY5Ybr4rj58+fDnF3gxK4YZ5VFZmZ5eXn0MSQpKYleGI0UFxfTx+666y6Ys8oidoEYu0jUzGz69OmOVxcpFAp5XRjNLmYzM/voo49gzj4/djGm6yK/NWvWOF4dlpCQ4HVhNLuo3cxsypQpML/22mth3rFjR5izi6vNottHZPny5TB3Hc+33347zFlFTDQXRbOqHyYlJQUe8+y79tlnn9Gx0EXXZmYvvfSS12tq0KABfYxVxLjExcXBC6MXL14Mt588eTId65VXXoE5u6iVVa36XiztEhMTA8/90VzQf//998OcFYqsXLkS5v369aNzsO+OL1Zlyi6CN+MXu7Pfx2guimYVhC5xcXHwGGKFA8OHD6djsapL9v1kx2I01amVpb8IiYiISGBpISQiIiKBpYWQiIiIBJYWQiIiIhJYWgiJiIhIYHlVjRUVFdnq1asjctb/BN2iuwK7uv+aa66B+dChQ2F+2WWX0Tl69OhBH0NKSkps8+bNETmrWBs5ciQdKzU1FeasMoTd5p1V9pi5r9RHioqK4Puenp4Ot2ftQMzM8vPzYX7dddfBnFVnuSqR+vfvTx9jwuEw7M30xRdfwO2HDRtGx2KVJvfddx/Mr7/+epifcsopdA5XVSCyf/9+W7JkSUTOevGx12RmtmjRIpijFiVmZr/8gu/I7+oX56qYQfbu3Wtff/11RH7EEUfA7UePHk3HYt9Pdox++OGHMEd9syqw/mvRYNWFrG2NmVmrVq1gPmTIEJizlg4nnnginQNV7LlaGx04cAD2q2P9FFl1phnvpcbOJ6z61tXm5qSTTqKPIeXl5bBSmlVHufpkst9B9rmOGDEC5rfeeiudw/VZMbt374bnTNR/zMzdhgatGcz4Z8JyVwUqOgf57Lf+IiQiIiKBpYWQiIiIBJYWQiIiIhJYWgiJiIhIYGkhJCIiIoGlhZCIiIgEllf5fGJiIiyVZyWOrmaTZ599NsyfeOIJmF900UUwR6XS0WKN5lhZ7eOPP07HYqXJrHyelQb27t2bzrF06VL6GJKYmGgtWrSIyN944w24/YMPPkjHYiXkNWvWhDlrDnn11VfTOfbs2UMfY0KhkMXFRR7WqJzXzGzDhg10LNbgcNKkSTAfM2YMzM8991w6R25uLn0MSU5OhuW47733ntdrMuOluAMGDID50UcfDXP2nTXzvwVCSkoKvKUCKwd3HSONGjWCOWtWzBp8su+ymXk1Mf49rPzapVu3bjBnTZF37twJ8x07dtA50K1AQqEQ3T4pKQmWyrPbMrz//vt0LHZ7FNZsm90m49FHH6Vz+IqJiYENQNFtLcx4ibyZ2b333gvzf/3rXzBnv4Ou5r/s9jYuNWvWtJNPPjkiv+222+D2roao//jHP2DOSv7feecdmN988810DlRy7zpGD6a/CImIiEhgaSEkIiIigaWFkIiIiASWFkIiIiISWFoIiYiISGB5VY2VlpbCZpus8SGrRjIz27dvH8zZ1f2sGqBv3750jhNOOIE+hpSUlMDmcezqc1SdVOGRRx6BeWxsLMxZkz3W6NKMN3ZlwuEwrExhzelYgz0z3oj2ueeeg3lRURHM16xZQ+eoXbs2fczX2rVrvZ+zdetWmH/22WcwRxV5rnHMzI466iiv18QaH0dTccSqDq+88kqYs6oY12foqkbyceGFF8J84sSJ9Dl33HGH12tq2rQpzLds2ULnOHDgAH3MF2tQyxpRm5nNmTMH5uw8wxrkuqrvfM8zrHl1UlIS3N713WTNVR9++GGYt27dGuZ5eXl0jurVq9PHkNLSUisoKIjIly1bBrfv3r07HYu9XlbZ+PHHH8P8ggsuoHNEUzXGnHrqqTAfP348fc6sWbNgzpp6s2pdVjlqhpuA+1SU6y9CIiIiElhaCImIiEhgaSEkIiIigaWFkIiIiASWFkIiIiISWF5VY7GxsbCX1D//+U+4vaviiVXSsKv7o6mK8ZWQkGDZ2dmVnvv888+nY2VlZcF83rx5MGd92f72t7/ROYqLi+ljSDgchlfSX3HFFXB7V0XTpk2bYD5u3DiYl5WVwZz1gzLzr1apmAdVBT300ENw+44dO9Kxpk6dCvOcnByYr1q1CuaXXHIJncP3uI6Pj7d69epVeo7hw4fTsVjvJ9Qnysxs0KBBMF+wYAGdg/WKYtgxeuyxx8Lt2ffJzGzy5MkwHzx4MMxZdY2rejIaZWVlsLdg8+bN4fZXXXUVHYt9hqzSjVU8ZmZm0jlQVSCrAjX77RitX79+RI4yM7Ply5fTsTIyMmDOqqfatGkD8yOOOILOwSrpXND5jFVbokrkCuycwaqw2PfJVdkYjdLSUtu+fXtE3q9fP7i9q9fZW2+9BXO2L6x6cv/+/XQOdJy4qroPpr8IiYiISGBpISQiIiKBpYWQiIiIBJYWQiIiIhJYWgiJiIhIYHlVjbGKDtZr6PXXX6djjRo1CuZz586F+UUXXQRzVk1SlVAlmZnZXXfdRZ/DruJ/9913Yc56prmufHddRY/ExMTAColt27bB7bt160bHmjlzJsxr1KjhNVZiYiKdI5pKiNjYWFhtxqoRe/ToQcdi+9i1a1eYu/reMagnk0tMTIylpKRE5Lt27YLbo75kFc466yyYs/2+6aabYO7aB98+TqFQCB7zrMrUVXXoW5HHqltcXBVBDKu+ZWO1bduWjsWqvdh3x7f/ohmumktISPAehx2jN998M30OqyBiVWOscotVrJmZlZeX08eQuLg4+LpY9eT9999Px2L78eSTT8KcVVp16dKFzsF6SbrExcVZWlpaRL5z5064vasv5IcffghzVp2am5tbiVf43zZs2BCR+Xz/9RchERERCSwthERERCSwtBASERGRwNJCSERERAJLCyEREREJLC2EREREJLC8yudjYmJguXOrVq28J0aNI814E8FPP/0U5q1bt/ae2xcra3U17GRlkevWrYN5NKW71apV834OUqdOHe/n7N27F+YrVqyA+ciRI2Genp5O5ygsLPR+XQxqxGpm1r59e/qcAQMGwPypp56C+bPPPuv9unw/w5KSElgazb5PLmPGjIF5z549Yd6uXTuYN23alM6xb98+79flMw4qm60wbdo0mPfv3x/m7LNYv349nSMpKYk+5ouVcbtuT8COuUmTJsGclbC7yuFRg+VommDXqlXL+zmsWSo777PbCbhKyNm5gWG3kXGVsDPslhvs1ijs9gAtW7akc7DPPBqsTN51qxzW6Pdf//qX19xLliyhj6HbaIRCoUqPrb8IiYiISGBpISQiIiKBpYWQiIiIBJYWQiIiIhJYWgiJiIhIYIV8GrKFQqFtZvbLn/dy/jJZ4XA4olRK+3fIgPtndvjvo/bvkHG4H6OH+/6Z6Rg91PeR7t/BvBZCIiIiIocT/deYiIiIBJYWQiIiIhJYWgiJiIhIYHm12MjIyAhnZ2dXevuff/6ZPsZuf52RkQFzVysGpqysDOaLFi3KRxdRpaamhhs2bBixPbu9v+vW5bGxsTBnY7HX2rx5czoHu71/bm4u3L+0tDS4f+x2+du2baNzs1vyb9++HeboFuhmZqmpqXQOdBt7M7PFi6K3y5MAACAASURBVBfD/TPjx2hRUREcy7WPrI3IgQMHYB4Xh79OWVlZdI4aNWrAPCcnB+5j7dq1ww0aNIjYnrUJcLVnaNy4McxZS5maNWvCnH22Zvw4YftXq1atcP369SO2Z+0nVq1aRedmbUeKi4thztoHuNqgsM/cdYympqaGUesIdk50tfhgnwk73n3O3xXQuWn9+vVWUFAAXzD7DrL3fc2aNXRudr5k3xv2eaSlpdE52OfOjlHf38GcnJxKb1shPj4e5qzNjauVTUpKCntd3udRdu7Ly8uj87PzOGsjws5L1atXp3Og7+i6dessPz+/Un02vBZC2dnZtmDBgkpvf+yxx9LH2I/4VVddBfNLL7200vNWYAuV2rVrw6vhGzZsaB9++GFE/v3338NxWA8VM37wfffddzBnB/J7771H52A93uLj4+n+TZgwISJHvYTMzF588UU6NzsRjBs3DuaPPfYYzM8991w6R0FBAczr1atHqxnYMcp+MF9++WU6/9y5c2H+448/wpz1bHO9jyeddBLMQ6EQ3McGDRrY2LFjI/Lx48fDcR5//HE69x133AHz4cOHw5z1Rfr3v/9N52AnNbZ/9evXh+8XW5SeeeaZdG52zmALizPOOAPm3bp1o3OwhXzdunXpMXrEEUfYO++8E5GzhdDQoUPp/L1794b52rVrYf7aa6/RsZjdu3dHZCeeeCLdPjs7G54zWV+4Cy64gI41b948mLO+Xmzxe+GFF9I52DHEjlHf30GfnlcV6tatC3P2frDfKDPeO5DtnxnfR/bHDdcxunPnTpiz3mH33XcfzDt37kznQMeDT+83/deYiIiIBJYWQiIiIhJYWgiJiIhIYGkhJCIiIoHldbE0s3r1api77lrNLiC77LLLYM4urHryySfpHLVq1aKPIWVlZfDCQHbRFXutZmZ/+9vfYD5s2DCYswuv2UWiZrxCgomPjzdUrcIsWrSIPsaqBNhFiewC40GDBtE5kpOTHa/Oz9atW2HuOn5uu+02mPfp0wfmqCLPzKxp06a/8+oqLxwOw4qg1q1bw+1d7+Hbb78Nc1ZkwC7IZhfIRyMpKclatmwZka9YscJ7rHfffRfmv/76K8zff/99mLOL9s3c1UhMUlKSHXnkkRH5Dz/8ALd3VeSwC9tZMcOtt94K82eeeYbOgSrTWFVshZiYyH9js+OKXQBsxi94ZxcAf/TRRzCP5nPyxS5YZpVeZrxqlVUR9+/fH+YzZ878nVdXNQoLC2E+bdo0+pxTTjkF5ldeeSXM2cXVrDioKugvQiIiIhJYWgiJiIhIYGkhJCIiIoGlhZCIiIgElhZCIiIiElhVUjXGesiwW6qb8f5WrNqB9fthV9eb8b5XTPXq1a1r164ROatEcBkyZAjMWduRiy66yHsO1quF2blzp3366acROWtzkZiYSMcaOXIkzFmfqvbt21fiFf43VukVDXYsuiobBwwYAHPWHsbVUqaqVK9eHc7DXpPrGGFVG67b9f/Z4uPjDfVSY5WpLqw1BqvCGjNmDMxdPY6ihapmMzMz4bauXlwMa7Hx8ccfw5z1kDLDVXPs/O0SzXn0zTffhHlubi7MWcuaFi1aeM/NlJSUwPMJO97uvvtuOtbChQthztpMsIrHn376ic5x1FFH0ceYvXv32uzZsyNy1jLH5fbbb4f5ySef7DWO61zGehFWlv4iJCIiIoGlhZCIiIgElhZCIiIiElhaCImIiEhgaSEkIiIigaWFkIiIiASWV/l8OByGZZOs4SNrtmbGS1LfeustmJ9zzjkwdzX/S01NpY8hJSUltmXLloh88eLFXuOYmfXo0QPmKSkpMN+zZ4/3HKw5HZOWlgabwY4YMQJu37dvXzrWt99+C/PLL78c5mz/XLc/aNasGX3Ml+97ZWbWu3dvmDdp0gTmn3/+OczZrR/MzGrXru31mvbu3Wtz5syJyOfPn+81jhkvpX7sscdgfvHFF3ttH439+/fb0qVLI/IdO3Z4j7V8+XKYs4bPDz/8MMxdx+jmzZu9X1c4HIa3HGGl1C6soSf7TM466yyYo2bTFVAz4fj4+Eq8uv9Wp04dmLtu03HGGWfAHN0GxMzsgw8+gLmrfJ7daoCJiYmB32l2nLhuHXL11VfDnJ2v2PuBbvvyR1SvXh3+hrma8zKPPvoozE844QSYs8+jXr16dI4/2qBbfxESERGRwNJCSERERAJLCyEREREJLC2EREREJLC0EBIREZHA8qoaC4VCXtUCL7/8Mn1s3bp1MB88eDDMWcO+o48+ms4RF+fXUzY+Ph5emT58+HC4/cqVK+lYrOHrlClTvF6TC2t264Ka091zzz1w2+7du9NxWBXGu+++C/Mbb7wR5q5ms9FU5DCsIeoll1xCn9O8eXOYs+P62muvhfmsWbPcL85DtWrVrGPHjhF5z5494fa9evWiY7H9YNVvrOGjy88//+y1fXJysrVt2zYiR5mZ2YcffkjHGj9+PMxRE1Ezfry7qv4KCwvpY0xsbKzVqlUrIj/ttNPg9v3796djsfMoa1hco0YNmNetW5fOgSrKXJV0zKBBg7znZtWmqHLSzGzy5MkwZ42lf29+JBwOw2bNrILZVfHIKua++eYbmC9btsxr+z8C7SNrJs4aFpvx6lvW9JlVgL3yyit0jm3btkVkpaWldPuD6S9CIiIiElhaCImIiEhgaSEkIiIigaWFkIiIiASWFkIiIiISWF5lVeXl5bZ3796IPCEhAW7v6p3DKjTWr18Pc1Y1lp2dTedAfbVcysvLbf/+/RE5q5AYNWoUHYs9xqrGvvvuO5i7Krfy8/PpY0g4HIZVYzExeD3sqgRg1XrsWGBjTZs2jc7Rr18/+hhTUlJiGzdujMhZ1RHrbWdm9uKLL8KcVd4cOHCAviaGVRcyMTExsE8fOxbS09O9xjfjfQCvv/56mKP3u8LMmTO950fWrFkD86OOOoo+h1XxsUokNodLND3eGFaVx3rbmfGqxzfeeAPmubm5MHf1OkTfaVdFTnFxseXl5UXkjRs3htsPHDiQjvXZZ5/BnJ33ozne0DnRJS4uztLS0iq9vasqbdKkSTBnvcbYe8U+bzPe/9GlvLzc9u3bF5Gz3ojTp0+nY2VkZMC8U6dOMGeVpq79QH3LfKrG9RchERERCSwthERERCSwtBASERGRwNJCSERERAJLCyEREREJLO+qMVQZgyqtzMwmTJhAx2KVKazXGKuqSk1NpXNEA1UQpKSkwG1Z/ywzXo3UqlUrmDdo0ADmrkoWV8UMEgqF4JX0rGKkfv36dKyJEyfCnFVIsdfqqvqLRnl5Oez/xPqysSo3M7Nhw4bB/IYbboB5jx49YM76QZn59zliWGWGqwfRCy+84DVHhw4dYD5v3jz6HPZeub47SNOmTWF+11130eeEQiGYswqXaKprTj31VO/nMOz75jpGi4qKYP7ll1/C/N5774W577mE9cgy+62iDFUxsqqxcePG0bFYL0JWEdi1a1c6FuNbfXvgwAHY86t169Zwe5abmb3//vswR/3dzHjfuXbt2tE5osH64TGsktbM7IEHHoA5q9ZjPRC7detG5/Ct/DuY/iIkIiIigaWFkIiIiASWFkIiIiISWFoIiYiISGBpISQiIiKBpYWQiIiIBJZX+XxcXBwt00VYQzkzsyeeeMJnanv88cdhzsoJo8EaWjKuBn/sfXr33Xdhzsq7XaXXBQUF/MUR4XA4ImOlj+eddx4dhzVLHTJkiNfrce0Davr3exITE6158+aV3v7II4+kj2VmZsL83HPPhTlrIujax7Vr1zpe3R933HHH0cdY48gVK1bAnJWjs7JoM7OlS5c6Xt0f99RTT9HH2HeZ3Tbg/PPP956fvVfRYE0iV65cSZ8za9YsmA8aNAjmvXv39n5dqBE2O1+ZmVWrVs06duwYkbNj/bLLLvN+Tddddx3M0fnNNbeZWZ06dbzmTkpKcpbEH4ydR8wMNqc1M7vzzjth/uqrr8Kc3X4lWuxWOcnJyXD7Y489lo7Fmqiyfbzmmmsq8Qr/265duyIy1iwd0V+EREREJLC0EBIREZHA0kJIREREAksLIREREQksLYREREQksELsKnu4cSi0zcx++fNezl8mKxwOR5QKaP8OGXD/zA7/fdT+HTIO92P0cN8/Mx2jh/o+0v07mNdCSERERORwov8aExERkcDSQkhEREQCSwshERERCSyvFhsZGRnh7OzsKpmY3Xa7qKgI5i1btoR5UlKS99w5OTn56CKqqtw/dkv30tJSmLdo0aJK5jX7a/ZvyZIlME9ISIA5a2URE+O/Fmf7Z1a1+7h161aY79+/H+ZZWVlVMq/ZX/MZLlu2DObsM2zWrFmVzGv21+zfqlWrYM7OGaxNwV91jLLrNVlrEzOzzZs3w5y1wGjYsCHMY2Nj6RzIunXrLD8/H74wtn979uyBY7FzvpnZhg0bYF63bl2Yp6enwzw+Pp7Owd73hQsXeh2jPi0dKmzcuBHm+fn5MEetS6JVledR9rtmxtvQsGO0Q4cOMHddz4y+I65j9GBeC6Hs7GxbsGCBz1Mo1puELSAmTJgAc1evKCYUCsGr4aty/y666CKY79y5E+afffZZlcxr9tfsX6NGjWDOvjyff/45zH16u1Vg+1cxP9pHdpJy/QCMHj0a5mwRyHpY+f7ImP01n2H37t1hzn4s2XcwGn/F/p199tkwZ//o+Oc//wnzatWqec8dzTHKfkxYDzIzs8ceewzmrIcV275WrVp0DqRLly70sezsbJs/f35Eznozrlmzho513333wfyGG26A+SWXXALz+vXr0znY+16jRg2vY3T37t1wHNcC6aGHHoI56ylWVd8Ns+iOUYb9o9GM9wNFPezM+D66+tuhf7y5jtGD6b/GREREJLC0EBIREZHA0kJIREREAksLIREREQksr4ulmaVLl8J86tSp9Dns4rzatWvDfNOmTTCP5mJpl/Ly8oiM7Z/rAsN58+bBnF1k/H+JXcx355130uc0btwY5oMHD4Z5NBdFR2P//v32ww8/ROSZmZlw+8LCQjrWLbfcAvMrr7wS5tFcFL1u3Trv5yCsymTEiBH0Oaxy89JLL62S1xSN0tJSKygoiMjZ5/T666/TsaZPnw7zvn37wjyai6KjUVpaatu2bYvI69TB3QAmTZpEx3r++edhPn78eJj7XhRthi9edX1vCgsLLTc3NyLv2bMn3H7AgAF0LFbtdd5558GcfYaLFy+mc7CKZF/sguGSkhL6nI8++gjmrFKR/Q4eccQRv/PqqgYrZmLFMGZmixYtgvm9997rNTerZq0K+ouQiIiIBJYWQiIiIhJYWgiJiIhIYGkhJCIiIoGlhZCIiIgEVpVUjbVt2xbm999/P30Ou8qcVYEcddRR3q8rGuhq/fbt28NtXVfKs2qg3r17R/W6qkJJSQnsbcNu4T9lyhQ6Fut/xG5rznoiuXrFRVOFlZSUZK1bt47I2T7OnTvXew52+3uG9Usy4y1JmOLiYvv1118j8rS0NLg9q0pxPefmm2/2ek2uFgK+n2FcXBysHGXHiWv/9u7dC3P2ff6rFBUVwfMDq5hlrVvMeDWmb3XYvn376GOo0tXVu4tVxX3//fdwe1f7C1f7DR81a9akj/n2qywqKoLVU82bN4fbDx06lI7FfidcfbUQ1rPMjPfQc9mzZw+suuzTpw/cnvUtNDM7/vjjYf7oo496vSZWGWtmlpGR4TXWwfQXIREREQksLYREREQksLQQEhERkcDSQkhEREQCSwshERERCSwthERERCSwvMrnS0tLYQkbK11zldUyl19+udf2f2ZJ3e9xlZwyxx13nNf2rATYzCwlJcVrrPj4eFhKuXLlSrg9K5E34/veqlUrr9fksmvXLu/nlJSUwMaErHx2/vz53nO89957MO/cuTPMXaWt6enpXnMnJCTAcuavvvoKbu86RtmxxXLf4y1aqOSe3YLA1dCS2b17t9f2rGmkWXSl+NWrV7euXbtG5Oy4ct1+gZWe+95uxPU+omawrvL5mJgY2PyUNcEtLi6mY6EGymZm7dq1gzk7Z7huJ+B7DmCNnRMTE+H2zz77LB2LNdr15dq/PXv2eI9XrVo1eD779NNP4fbsN8SMvy8Mu2WC6zYLf5T+IiQiIiKBpYWQiIiIBJYWQiIiIhJYWgiJiIhIYGkhJCIiIoHlVTUWFxcHK7GWLFkCt8/MzKRjNWnSBOYvvfQSzLt16wbz1NRUOkdVVY2xKhPX+KwZ4oMPPgjzxx9/HOZjxoyhc/Tq1Ys+5mP27Nkwd1X9saqR0aNHw3zw4MEwz8vLo3NkZWXRx5iEhARr3LhxRI6aQJqZffHFF95zPP/88zC/4447YO6qvisvL/eeH2HfA1cV3+rVq2F+/vnnw/yCCy6A+YknnkjnqFu3Ln3MB6ucYs10zcz69+8Pc1YF9tNPP8G8U6dOdA7UpDlarPknq5wyMzvppJNgfuONN8L8nnvugbmr+hZV67iqzFJSUuyEE06IyFFmZrZw4UI6FmsMzJpXDxs2DOau78Evv/xCH0Nq1KgBG4my7+AZZ5xBx2IVmgMGDID5McccA3N2rJtFV20VExMDf8N69OgBt3c1WGffN3ZeZPvCfiPN8HHiqkY8mP4iJCIiIoGlhZCIiIgElhZCIiIiElhaCImIiEhgaSEkIiIigeVVNVZeXg57FzVs2BBuz6prXFhfFFa58fTTT9OxrrnmGu/5UaUU61M1duxYOg7r8cSufP/uu+9g/tBDD9E5fKvGSktLraCgICJn1UCu969GjRowZ+/JLbfcAnO232a8sjAa69evh/ncuXO9x7r77rthvmPHDpjPnDmTjnXmmWd6zc2+g6znVTgcpmMVFhbCfPv27TB/4IEHYD5ixAg6x4UXXkgfQ8rKymCVJqs4atGiBR2LHVuXXHIJzHNzc2H+wQcf0Dn69u1LH2PKy8vhe9+lSxe4vaviifVxYvuek5MDc1ZVaWZ2/fXXR2SuXmMlJSW2efPmiHz//v1w+y1bttCxRo0aBXP2Xr344oswZ9VOZma33XYbfQyJjY2FFWLs+/TJJ594jW/Gq/tYdZbrHMPeQ5dQKAR7/rEqvnXr1nnPwaqCP//8c5i3bt2ajjVy5MiILCEhodKvRX8REhERkcDSQkhEREQCSwshERERCSwthERERCSwtBASERGRwPKqGtuzZw+8Op31RXFd5b1s2TKYz5kzx+clOfvEsMomprCwEPZNa9q0Kdye9dUyM3v55ZdhvnHjRphv3boV5q5qAF/79u2zefPmReT9+vWD29euXZuOtXPnTpizqgKGVeqYmbVr185rrAqo8o9V3rBqNjOz77//HubLly+HOatAQ+95tIqKimzt2rURedu2beH2xx13HB3r22+/hXl6ejrMU1JSYO7av7POOos+hpSWlsIqIlTBYmaw51OFr776CuasPxjre7d06VI6x4EDB+hjTExMjFWrVi0iZ9VT3bt3p2Pt2rUL5uy7u3jxYpivWLGCzjFo0KCI7Pf6EPr0t2LHoeux008/HebsPHrXXXfROdhYTFFRka1atSoib968OdzeVRk6adIkmH/88cder2nGjBn0MXZucGGVfw0aNIDbf/bZZ3QsVrGXnJwMc1Zpyo5dM/fxWBn6i5CIiIgElhZCIiIiElhaCImIiEhgaSEkIiIigaWFkIiIiASWFkIiIiISWF7l87Vq1aKl8ggrDTQz+/vf/w5zVi7JSvHvvffeSr+e31OtWjXr2LFjpbd3le6/8847MP/Pf/4Dc1b+6CrtZE0+Gd/PzzU+a4I7ffp0mLMmiW3atKFzsPLK34NKratXrw63ffbZZ+k4bF9uvvlmmLPy62uvvZbOwZ7DJCcne5XDDh48mD7Gbg+wadMmmNerVw/mrttkxMV5nWIsMTHR2Uj1YK7Gw6y0/bnnnoM5a1Dbp08fOoerWakv1mT49ddfp8955plnYD5s2DCYs7J613ettLQ0InM18/X1yCOP0MfY70R+fj7M58+f///au/PoqqqzDeDvzc3IIATClABhUGYBQQWp6EJFgUIFEYWqZdk6MIi6LFqHUhXHimOLRUVmFOtYRAuogBUUKEOQGaEYVMIUkDkhIbnfHyzWarnPs2HHfK4F+/n9+Zxzz77nnnPu3YTznhfm7JEJZu7zF0lJSaGl8shbb71Flw0dOhTmEyZM8HpP06ZN81r/ZJKSkmipPNKmTRu6rEmTJjCvU6cOzIuLi2HerVs3OgZ7vMap0l+EREREJFiaCImIiEiwNBESERGRYGkiJCIiIsHSREhERESCFfG5+z8SiewyM14qdfrIjsViNU4MtX+nDbh/Zmf+Pmr/Thtn+jl6pu+fmc7R030f6f6dyGsiJCIiInIm0X+NiYiISLA0ERIREZFgaSIkIiIiwfJ6/n3VqlVj6LHb7PHWRUVFdFs7d+6E+d69e33eEn1Mt5nRR4QvW7YsH91ElZGREWvQoEHc+uw+KlcLCrZ/hw8fhnmjRo1gXqlSJToGa1/A9i89PR0eP/Z4fdaiwMxs9+7dMN++fTt9DVKzZk26rF69ejBn+2dmVq1atVhWVlZczh6xf+TIETr+wYMHYb5161aYs2OF3s/JXlNe5yg738zMvvvuO+/XIOj9HFe9enWYs/1jxy8lJcXrPZmZffPNNzA/cOAAzNn3WO3atekYbJnrHE1PT4f7mJqaCreVl5dHx9+zZw/M2Xcvaw3hakGBztHc3FzLz8+PoPXZOcoUFBTQZRs3boQ5a8NQpUoVmLuOoe81yI4f+z7ev38/HZudi6yFSOXKlWHOrjPXMtc56nsMXfvIjmFycjLMs7OzYZ6UlETHQL9hrnP0RF4ToczMTJsyZUpcXq1aNbj+5s2b6bb+9re/wfz999/3eUt222230WWPPPIIzCORCLwbvkGDBrZ06dK4HPXaMTN755136NgvvfQSzHNycmA+atQomF988cV0jBo18A3xbP8yMzNhDzTWJ2b9+vV07EmTJsH86aefpq9BBgwYQJexPkps/8yOTTqmT58el7MfUtc5unDhQpj/4Q9/gHnbtm1h7uqlxI5vNBr1OkfZD9/y5cvp2MOGDYM52r4Lu87MzAYOHAhzdgzZ8WP/UHDp2rUrzD/77DOYsx+ZO++8k45x3333wfxk5+i7774blzdr1gyu//DDD9PxWR8rNsl9+eWXYc568ZmZderUKS5jvQPN+DnKrF69mi5j/aXYP0Y6d+4M83vvvZeOcckll8DcdY6+/fbbcTmbbM2aNYuO/fnnn8N87NixMO/YsSPMb7rpJjoGW+Y6R32P4aeffkqXXXnllTBn/0Bk56jrjx6o/6LrHD2R/mtMREREgqWJkIiIiARLEyEREREJliZCIiIiEiyvm6Wj0aidddZZcTm7EfW1115zbgsZM2YMzAcPHgzzGTNm0DGGDBlCl/mYO3cuzL/88kv6GlY1xu6UHz16NMz79Olzknd36tLS0uiN0YireohVmj322GMwHzFiBMznz59Px3DdjM4kJyfDajN2vi1evJhua+XKlTB/8sknYc7e77Zt2+gYX3/9NV3mg52j6KbO41hVCCsOWLFiBcw3bNjgfnMeUlJSvG6M/uijj+gytp1du3bB/I9//CPMFy1aRMdgNyu7pKamwhuj2bngqsRklXHsRvFBgwbBfOLEiXSMtWvXxmWuilKGVQ+5zlF28zOrIFqwYAHMXVVxrAKNSU1NtRYtWsTl7Ds/NzeXbotdU+wGZ3bjtevGYFb0URYzZ86E+e9+9zv6GlaVV79+fZiz65AVOZQH/UVIREREgqWJkIiIiARLEyEREREJliZCIiIiEixNhERERCRYXlVjKSkpds4558TlX3zxBVz/7rvvpttijwqPRHBrEHa3uuvx/q4+Vj7Yo9NRBd1xf/nLX2C+adMmmLPeMqyHlBn/rJiioiL74Ycf4nK2H+3ataPbYsvYfrCqsQ4dOtAx+vXrR5cxR44cgZ9x8+bN4fqsusYMtxYw4/2dtmzBT6xn1RFmZueddx5d5oOd667rg7WUGDduHMxLSkpgztpMlMXRo0dhHzvW169nz550W2wZa+nw6quvwpxdy2Zm/fv3h7mrdUxBQQF8D6zFhqttDXvP//znP2HOKnJcUIUU64vmwq6DkSNHem+LVdOyXmNNmjSh23L1sEIKCgpghR+ryL3hhhvotthvJKvEvuiii2Du2j/2mrJgvRlZVbcZ/+5nLX7YfIJ9X5UH/UVIREREgqWJkIiIiARLEyEREREJliZCIiIiEixNhERERCRYmgiJiIhIsLzK50tLS+3gwYNxOWuq9u6779JtsdJkpnXr1jD/4IMP6GtYc0VfrGw4IyODvqZOnTowr1q1KsxZc8FevXrRMVyl50hiYqJVr149Lv/000/h+qxU0oyXqb7++ute74k9RsHMbM6cOV7bMjtW1otK5VlDVNcjFj7//HOYs3Jb1qTWdZ6UF1a6y5pympldffXVMGel0atWrYL5/fffT8dgTZQZdo6yY+FqaMsa6roa/SKZmZl02bp167y2ZXasYXGrVq3i8nnz5sH1u3Tp4j0GKnk3M8vJyYH55s2b6bbYd5OvxESvnxsz48089+/fD3PUcNmMNzc1M7vyyiu93lNqaqq1bNkyLmcNgFkTYzP+6BL2vbhkyRKYo0dOHLdv3z66zFf37t1h7noMydSpU2HOmpazJs6ssbSZ2WWXXUaXnQr9RUhERESCpYmQiIiIBEsTIREREQmWJkIiIiISLE2EREREJFhet/EnJCTACjF2J/uECRPotlgDtQMHDsB80KBBMP/FL35Bx3A1okMKCwthlQ27sz85OZluizXTW7t2rdd7YhVrZYWauLL39Oijj9Lt9O7dG+YzZsyAebdu3WDesGFDOkatWrXoMl+oWbCZ2R133EFfs3DhQpiXlpbCfNSoUTB3VRK5iwAAHgVJREFUNV3Ny8ujy3ywxqCzZs2ir1m/fj3M2efOrll2bM38GwMzrBrRtX+s+q2wsBDmrHFkhQoV6BhlaexcUFBgK1eujMtRtZyZ2a9//Wu6LXaObt++3es9sWpWM9zw9mTfS+gamTZtGlx37969dDvjx493jnMi1lyZVZOVxdGjR23Hjh1xOWuQzRrEmpldeumlMGffMayBqqt5M2sS7VJaWmqHDh2Ky1nz8+zsbLqtm266Ceas2pxVK7t+b38q/UVIREREgqWJkIiIiARLEyEREREJliZCIiIiEixNhERERCRY/s1fgHbt2sH8448/pq/p2bMnzJ988kmYs+oi1oPMzL9yIjk52bKysuJydtc963djZrZgwQKY9+vXD+as2oFVrJnhag6XhIQEWAHDKtxuuOEGui3Uc86MV+q88cYbMGdVCOWNfb4jR46kr/nqq69gzqrpateuDfOUlBQ6hquPFRKLxayoqCgu79GjB1y/bt26dFuffPIJzCdPngxzdsxdvZpYFSgTi8VgbybWK66goIBu66mnnoI5+15ivQlZf6WySktLg99brHrqmmuu8R6jadOmMGfVPa4KzfT09LgsGo06x0fVgjfeeCNcd8uWLXQ748aNg/nFF18M87PPPhvm7Povi6SkJPg7wXoKuqpv2fWfn58Pc1RtaGZWo0YNOoarMpdh1yH7vXX1OmNYNRmr9mbHvDzoL0IiIiISLE2EREREJFiaCImIiEiwNBESERGRYGkiJCIiIsHyqhorKSmBlUqsjxO749/MbNu2bTC/7rrr6Ni+WO8eJiEhwSpWrBiXsx4nv//97+m2HnroIZiz3kCsVxSqEDoOVXOUBav0cvV2Wb16NcxbtGgBc/Z5uLBzpCySkpJgzqprzMw+/PBDr9ewikBUfXEc60/ElJSUwEqstLQ0uP5VV13ltX0zftxZZZoL60/ma+vWrTB3naOsGmnEiBEwb9++vff72rBhg/drGNZf6tprr6WvYf3tUC8sM7M5c+b4vzFPxcXF8NplPaRcVU3sO4BVaN11112n8A7/f7BKuqFDh9LXsOPHKjRZVXWDBg3cb85TYWEh7EXIflMbN27sPQb77mNVzP+f9BchERERCZYmQiIiIhIsTYREREQkWJoIiYiISLA0ERIREZFgaSIkIiIiwfIqn49Go7Bkm5W2olL045544gmY16xZE+as7LxatWp0jI0bN9JlSHFxseXl5cXlrDHe9OnT6bauv/56mF999dUw37x5M8x9m3K6lJSUwEaxrHmsq+Hr22+/DXPWvPH5558/hXf4v3wff+CSkIDn/D/88AN9DSu/vvnmm2FeXFwMc1bKbOa+RpBYLAbHqV+/Plx/4sSJdFvPPvsszDt27Ahz9hiAxET+NXLo0CG6DIlEInB76Lo0M+vSpQvdFrt2WEl2YWEhzF0NJevVq0eXMUVFRZabmxuXsxLoGTNm0G19++23MH/11Ve93tPOnTvpMvadzESjUatSpUpczq7B2bNn0201a9YM5uyxEN999x3M2fVRFuzxAHXq1IHrs0apZmbz5s2Dea9evWBe3mXyTGpqKmxUy/ZlxYoVdFus4e3TTz8Nc/aZdOrUiY7hamx9KvQXIREREQmWJkIiIiISLE2EREREJFiaCImIiEiwNBESERGRYEV8mj5GIpFdZoZLaU4v2bFYrMaJofbvtAH3z+zM30ft32njTD9Hz/T9M9M5errvI92/E3lNhERERETOJPqvMREREQmWJkIiIiISLE2EREREJFheLTaqV68eQ4+UZ4/Ydz1anD2unz0Wv3bt2jA/cOAAHYO1L8jJyclHN1FVq1YN7h9rE+B69H6FChVgvm/fPpizR4Q3bNiQjnHkyBGYr169Gu5fenp6LCsrK2791NRUuJ01a9bQsZOSkmDO9iM7OxvmBQUFdAzHeQX3z4zvIzvfIpEIHZ+9N9ZSho1x7rnn0jHY+GwfMzIyYuizZNv58ccf6djs/I1GozBnx5C1TjA71k4CWbVqldf+sfYXe/fupWOzz4Qdvxo18H2VrHWCGb8Oli1bRs/RjIyMGGr5UFJSArfFvjPMzPbs2QNzdgxZSyLUOuk41NLl+++/tz179sAPOCMjI4ZaQbBz4eDBg3Rs1jKDfVbsGLpabLD7ZJcvX07PUZ+WHa79Y61j2PFjv4+uVj3s2lmzZo3zHPVp5+FqpcPat7Brl322vi2XcnNzLT8/n3/B/xeviVC9evXsk08+ictZLxpXH55du3bBfOjQoTB/4IEHYD537lw6BuuZVLFiRXg3fL169WzmzJlx+dKlS+F2JkyYQMe+4IILYM76BrEJz5tvvknHYP3JGjduDPcvKyvL3nvvvbi8adOmcDutWrWiY7Nj3qRJE5i/8sorMF+9ejUdg305161bl1YzZGVlwT5ovj8YZmZr166FOTsX2Tn94Ycf0jHYJLROnTpwH7Ozs23x4sVxOZs0ouN93JQpU2DOesyx/lVpaWl0DNRTy8ysYcOGdP9QX8H169fD7bj6/bFJCjt+1113ndf6ZsfONyQSidBztH79+jZ//vy4nPX8++ijj+j406ZNg3nVqlVhznogstwMTxx79OhB12/QoAH8zmR9/b744gu6rWHDhsGcXc/sGI4ePZqOwf5BmZqaCo9h/fr14XtmE++vvvqKjv3www/DnF2Djz32GMzZ740Zv3aaN29Oz1F2DJlFixbRZeyzZ7+FI0eOhPlNN91Ex0AT4w4dOtD1T6T/GhMREZFgaSIkIiIiwdJESERERILldY9QYmIivBmN3Wzm+n/LDz74AObsBuu+ffvCfNSoUXSM5ORkugwpLi627du3x+WNGjWC6y9ZsoRui92fwG6iZv/Xf//999MxXDfIIampqfB+IHbT7BVXXEG39dJLL8F83rx5MGf3l7huBHXdgOeL3e80cOBA+prGjRvDfMiQITB/4YUXYD5mzBg6hutGaiQSicD7gdgxnDNnDt3Wv//9b5izm6LZ/7m7iiJcxQw+2HdMRkYGfQ27pti9iy+//DLMhw8fTsdw3ezvi90jNGLECPoadi8J+25g9zu5zkNUAFFaWkrXZ9j5dsMNN9DXdO/eHebs/j12DNm9NWbuG8WRhIQEq1SpUlzObsK//fbb6bZYcUnr1q1h/tvf/hbmq1atomOw+znLgn3uH3/8MX0Nu97Y/ZmPP/44zF33CLnu9TwV+ouQiIiIBEsTIREREQmWJkIiIiISLE2EREREJFiaCImIiEiwvKrGYrEYbCPAKqTuuOMO7zfEKj3YXf+uJ0vfcsstXmMnJyfDx3tXrlwZrt+rVy+6LfaYcHbX/V133QVzVj1g5q4U8MEeXd6uXTvvbbHqHvbUVdeTs1mFhEs0GoVP1WVtIPr370+3xdoRTJo0Ceasgoc9Ld3MLD8/ny7zwY6hqxqItVDp0qULzJ9++mmYb9lCH1BLq2KYkpISWEnYpk0buL6rvQf7bPv16wfzqVOnwpw9/dvM/VRtJiEhAVZ1saeDt23blm6LHd9atWrBfMeOHTBnFZJmBitpXa1pGNYewtXKgR2rTz/9FOasAsxVGVZe1yBrB4JalBx39913w5x9Jq5KZYa1uCiLFi1awPyiiy6ir3nooYdgztr/nHfeed7vKycnJy47fPjwKb9efxESERGRYGkiJCIiIsHSREhERESCpYmQiIiIBEsTIREREQmWJkIiIiISLK/y+cLCQlu3bl1czkrqXCWLCxcuhDkry2Slu6y80sxs06ZNdBmSkJAAm6KyMj9XWfSDDz4Ic9bQ8sUXX4S5q0Tet2Enaypbu3ZtuD4rWTYz69q1K8zZ8evTpw/Mu3XrRsdAj2o4maSkJFimm5ubC9c///zz6bZYs0v2nl955RWYT5w4kY7hajhZHgYNGkSXsWaprIHif/7zH5i7SsjZ+c6w0nL0vWPmLuPetm2bV44aSpuZHTx4kI5RnurWrQvz++67j77m73//O8xLSkpgzhqfLl26lI6BrhHfhtZmZh07doT5W2+9RV8zbtw4mLNGppdeeinMy/N7lGENtV2PkWGNdl9//XWYL1u2zPt9NWvWzPs1vnr06EGXDR48GOY333wzzMePH+89Piq5Z8cD0V+EREREJFiaCImIiEiwNBESERGRYGkiJCIiIsHSREhERESC5VU1lpaW5mwCeiLWgNMMN/Iz400UW7ZsCfMqVarQMaLRqOPd4bHRnebs7nNWGWbGK7Hat2/v9Z7Kq6LB7Nj+uRpInsjVjJA1PWSNWv/85z/D3NVwsTwtX74c5n379qWvueeee2DOql9Y01VWHWHGG/r6Yg0Gp0+fTl/DqtxYNWRWVpb/G/N09OhR27NnT1zevHlzuL6rImfMmDFe+eTJk2F+9tln0zF8GjueDKtOZc1gzcy+/PJLmD/66KNeY7uqJ32VlpbagQMH4nJWrfePf/yDbmvs2LEwZ79DrGqsPL9HGdZU1nWNs2uN/d79nNDvN6ugzMvLo9thzWhdv90/N/1FSERERIKliZCIiIgESxMhERERCZYmQiIiIhIsTYREREQkWF5VYwy7k5z1MjLjFSusMqVXr14w3717Nx2jWrVqdJkP1qfGVYH17LPPwnzWrFleY8+ePZsuu+qqq7y2FY1GrWrVqnE56zP0xhtv0G098cQTMEfbN+M9tVjvo5+itLQ0LmM9rwYMGEC389xzz8F8xYoVXu9nzZo1dBmrQPO1YMECmL/22mv0NawHUKVKlWDO+rWVZ+VfcnIy7Lm1detWuD7LzXgFI6vOqlWrFsxZjzXXa8qCVTYuWbKEvuaaa66BeVFRkdfYru/R6tWre23LDFf/sqox1lfLjH+Hs++s4uJimCclJdEx9u7dS5f5YO+JXZtmZm3btoU5+45h566rr6fvuXAc6uNXWFgI133hhRfodu6++26Ys6pk9j3D+ueZmTVu3JguOxX6i5CIiIgESxMhERERCZYmQiIiIhIsTYREREQkWJoIiYiISLC8qsYKCgps9erVcXmrVq3g+q6KoEaNGsF806ZNMGd9nNgd5mbuO+l9sJ4o8+bNo6/5+OOPYf7MM8/AvFOnTjBv06bNSd7dqTt69Ci8U5/1GXJVG3Tp0gXm9957L8x/rp5iZrhipaCgAK67YcMGuh1W7TFnzhyYt2jRAublVRlmdqxyAlW5NG3aFK7vqqrq1q0bzFmlGTsXf45jy6pJb7vtNvqaUaNGwZxVZ7Fr0IVV2LnEYjFYfdOsWTO4PvrOPY6dc4sXL4Z5w4YNYd65c2c6hq+ioiL7/vvv43J2jrKqYzNepfT222/DfMKECafwDv8Xq3RliouLYQXchRdeCNfv168f3VadOnW8x/aVnJzs/ZojR47Yxo0b43LWCzQtLY1ui/Vae/XVV2H+y1/+Eub9+/enY/xU+ouQiIiIBEsTIREREQmWJkIiIiISLE2EREREJFiaCImIiEiwNBESERGRYHmVz6elpcFS+e+++857YFZmfcUVV8CcNRhljRXN3E3afNSvXx/mhw4doq8ZOHAgzG+99VaY165d2/t97dmzx2v9xMREy8jIiMtZU9mWLVvSbV122WUw79ChA8wffPDBU3iH5QM1Xb344ovhuq7GtexRB5mZmTAvS5nqjh07vNZnjXPZufjkk0/SbT3++OMwZ+Xw5dXEuDxt2bKFLovFYjAfO3YszFkJcDQapWOUpZw5EonAhs3sc7/nnnvotqZOnQrzvn37wtx1TZeXxMREq1mzZlzOzh9XefmUKVNg/t5778EcNQotb0lJSbDsnT2yYMyYMXRbw4cPh/mf/vQnmO/cuRPm6PP+KVJSUuycc8455fVdzYfZserZsyfMmzRpcsrjlhf9RUhERESCpYmQiIiIBEsTIREREQmWJkIiIiISLE2EREREJFgRVlkBV45EdpkZL9M4fWTHYrEaJ4bav9MG3D+zM38ftX+njTP9HD3T989M5+jpvo90/07kNRESEREROZPov8ZEREQkWJoIiYiISLA0ERIREZFgebXYSE9Pj6H2Aqy1wIoVK+i2UKsHM4PtA8zMqlSpcgrv8H+xFhsrVqzIRzdRZWRkxNhj7pEffviBLjt69CjMK1WqBHP2eZTFsmXL6P5lZ2fHrc8eS5+Xl0fHOHLkCMxr1MD3prH9Lgu2f2Z8H9m9cK72MKgNgitn564Le1/Lly+H+1i1alV4DVaoUAFuZ+PGjXRs1h6iRYsW9DWIq5UNO7dycnK8rkHUNsXM7Mcff6Rjb926FeZnnXUWzNmxaNiwIR3D9/iZ8X1k28rPz6fjszY77PpMSkqCuet7D7Ueyc3Ntfz8fHhwfb9HN2/eTJcVFhbCvFGjRjBn12ZZuL5HffaPnYdm/Niyc5Sdi657fdn1+fXXX3ufo8zatWvpMvYdwH4r2G8h+w4wM0tIiP+bjuscPZHXRCgzM9PefPPNuJx9YK4fhj59+sD8V7/6FcxZXxKXvXv3wjw9PR3eDd+gQQNbunTpKW+f9UszM9u9ezfMO3fuDPObb775lMc9mUgkAvcvOzvbFi1aFJezL8dHHnmEjvHNN9/AfMiQITBnvb7Kgu2fGd9H9qM/ePBgOg6bEDRt2hTmvXv3ptti2A9Wamoq3MfMzEzYf6l9+/ZwOz169KBjs4m8zzVgZrZ//366LDERf8VUrFjR6xpkvdTeeecdOvaIESNg3rVrV5izc2Ty5Ml0DPYjk5SURM9Rto/sH0/jxo2j47NeY7m5uTBnPakmTpxIxzj33HPjsvPPP5+u7/s9OmDAALpszZo1MH/rrbdg7juJd2HfM77798ADD9Bl48ePh/nll18Oc/T7a8bPHTP+O1ijRg3vc5Rp06YNXZaSkgJz9t3LfgsPHDhAx6hcuXJc5jpHT6T/GhMREZFgaSIkIiIiwdJESERERIKliZCIiIgEy+tm6bS0NHhTFLupit0QbWY2duxYr3z48OEwHzVqFB3Dt4onFotZUVFRXM5uDHbdxZ6TkwPzVatWwbw8b5ZmYrEYvDmXVYcVFBTQbbFjPmzYMJizGz7btWtHx0DH4mSKiopgJRiqJDMze+ihh+i2rr32WpizSrMHH3wQ5vfddx8dY926dXQZEolE6M2HvttnN0uzG5D79esHc1RVdJyroswH2w/XdTNp0iSYP/zwwzCvVq0azF03orJCg7JYsmQJzNl+mJk1btwY5qxYY/ny5TDft2/fSd7dT7d69WqYu6qq2HHv0KEDzLdt2wbz8qxaZdj3woIFC+hr2H5MmzYN5vPmzYM5228zs+rVq9NlDPutWLx4MVzfVWH24Ycfwpyd76yAZNCgQXSMn0p/ERIREZFgaSIkIiIiwdJESERERIKliZCIiIgESxMhERERCZZX1VhxcTG8w79+/fpwfVY5ZWaWlZUF89GjR8N8w4YNMGdVEGbuiiSkoKAAPtL9vPPOg+uj/ib/vS2E7UdZfP/9917rJyQkwOoJVsnG7t434y0zJkyYAHN2LriOEeth5xKNRi09PT0uZ60emjRpQrfF2lawzz0ajcLcdczbtm1LlyFpaWnWqlWruJy1WnBV/r388sswZ++XVU+5qqrKcgyR559/3vs17Nxi7SeaN28Oc1dlmGvffbFtXXnllfQ1qO+cGb922fEozxY4DLtu5s+fT1/D+k6xNjesBcX1119Px/DtY1laWgqvK9ZqxtX/jPUIY7857Ht04cKFdAzf7xgzXp3aunVruL7r/GG95FiVJvuudvUVRN/5PvQXIREREQmWJkIiIiISLE2EREREJFiaCImIiEiwNBESERGRYGkiJCIiIsHyKp83O1ZWdyLWvPHss8+m23njjTdgzppgvv766zDv27cvHYOVJjIVKlSAZYusBPn222+n21q2bBnMe/XqBXNWOrt37146Rr169egyH6wU9fzzz6evcTVKRGbNmgXzHj160NfUqVPHawwz3jiXfb6s5N2Mn4sTJ06E+eOPPw7z/v370zEOHjxIl/lgDYZdZaXvv/8+zGfPng3zAwcOwPz++++nY7DmvL7YZ8vOKzPeLJlhJdau5sqsuWlZdO7cGeausuEbb7wR5uxYvfDCCzCfOXMmHaN79+50mY+OHTvC3PU7wcqy2TXI9ttVQt6oUSO6DIlEIrDEGz3WwszsqquuottijZ3ZY2FWrlwJ8xYtWtAxyvMRD+x7hjWPNTObPn06zL/66iuYs2vq0KFDdAz0W+zz+6+/CImIiEiwNBESERGRYGkiJCIiIsHSREhERESCpYmQiIiIBMuraqy0tBTeuc2aGz7xxBN0W6wS69JLL4U5qxpzVd2UV0VHWloazHft2kVf8+KLL8Kc3cnOKsDmzZtHx2ANCX2x5nesIsXMbNOmTTBnFTZPPfWU13bMylY1lpSUZLVr1/Z+HcKqWW655RaYT5s2DeZLliyhY7gqSnz07NkT5qwhshlvoMiO1YwZM2DuqopjjWt9bd++HeasoaMZr3BhFTkvvfQSzAcMGEDHqFWrFl3ma9GiRTDft2+f9/iXXXYZzFHVrxmvWCtP7LuPNWo241Vj48aNgzmrAs3Ly6NjXHjhhXQZUlhYaGvXro3Ls7Oz4fqsWs6MV1xfc801MP/2229h7mqQXbNmTbqsvKBK3eP++te/wpxdn6yKz1UBixrbsnMd0V+EREREJFiaCImIiEiwNBESERGRYGkiJCIiIsHSREhERESC5VU1lpKSYuecc05cznrh7Ny5k26L3alft25dmE+ePBnmrHrAzOzZZ5+ly5CSkhLY24vd3X7RRRd5bd+F9c655JJL6Gtcny/C9o/153H1MtuzZw/Mhw0bBvM+ffrA/LPPPqNjlGclC6ryMOP7YWbWpk0bmI8dOxbm7Fixc9fMrHfv3nQZcvToUcvPz4/LzzrrLLg+qwxzeeCBB+jYCKtkMTPYu8/l8OHDlpOTE5ez6ih2bZqZ/etf/4L5+vXrYd64cWOYJycn0zHQsTiZWCxmxcXFcXmlSpXg+s2bN6fbatCgAcxZ1RHrScXGNjtWJXUiVx+n4uJi27FjR1zOjiGrDHNJSMD/hmeVnuicOs73GkxOToafO6vcGj16NN3WpEmTYM6uqeHDh8P88ssvp2OUpWqM9Wxkn3tWVhbdFqroMjNr2LAhzIcOHQpz9r1rZvab3/yGLjsV+ouQiIiIBEsTIREREQmWJkIiIiISLE2EREREJFiaCImIiEiwvKrGGFaxwqpuzHjFE6sUQtVqZmZXXHEFHSMlJYUuQ6LRKKxCmTNnDlzfdac+q6R75plnYM76fbnuxndVbiBs/1auXAnXd/VqYRU5s2fPhnlJSQnMt2zZQsdw9XLzxfqyoSq641ilCat0e+2112COKmiO8606SkxMhD13WP+ssozdqVMnmM+cORPmn3zyCR0jMzOTLkMSEhJglcnhw4fh+gMHDqTbYtctqw6rWLEizF19lMqiqKgInvfs+2r+/Pl0W+vWrYM5681WlipC3z5O0WjUKlSoEJcvXLgQrt+qVSu6rRUrVsCcndf79++HOatQMuPf1Qyrvq1RowZc31Xdy47trbfe6vWe2rZt67X+yUQiEVgt+fXXX8P1mzRpQrf13nvvwZzNG1j/QDYHKA/6i5CIiIgESxMhERERCZYmQiIiIhIsTYREREQkWJoIiYiISLA0ERIREZFglUv5fDQahXmvXr3oa/Ly8mDOShnfeecdmJelHNQXK5N3lc+zktulS5fCnO3fddddR8coS8NHhJVL33nnnfQ1lStXhjkrq69SpQrMW7ZsScdgDf7KgjUeZCXvZmZbt26F+SuvvOI1dvfu3ekyVAp/Muh6Y49fGDJkCN0OO0efe+45mLPmvKwc3czdzBNhj3hg5fPffPMN3RZryMqamLIy7oMHD9Ix2GMZXFJSUmBz0N27d8P12XeGGX98CHsMCbtuXVCpOHschtmx6xaN065dO7i+6zuutLQU5uwRFuzxJD179qRjJCb6/QxGo1H4fca2c8EFF9Btde3a1WvsuXPneq1f3tgjcVy/w+wRGqwZdf/+/WHuelQOemyC6xw9kf4iJCIiIsHSREhERESCpYmQiIiIBEsTIREREQmWJkIiIiISrIhP485IJLLLzHiXzNNHdiwWi+uQp/07bcD9Mzvz91H7d9o408/RM33/zHSOnu77SPfvRF4TIREREZEzif5rTERERIKliZCIiIgESxMhERERCZYmQiIiIhIsTYREREQkWJoIiYiISLA0ERIREZFgaSIkIiIiwdJESERERIL1fxr1gghpe34dAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a16ffd0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_digits(filtered_digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.n_components_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
